A nutrition laboratory tested 25 "reduced sodium" hotdogs of a certain brand, finding that the mean sodium content is 310 mg with a standard deviation of 36 mg. Constr…

Question

asked Apr 3, 2021 182k views

1 Answer

Jastend · Answer 1 · 2021-04-07T15:00:56+0000

Answer:

The 95% confidence interval is
$295.9 < \mu< 324.1$

A 95% level of confidence mean that there is 95% chance that the true population mean will be in this interval

Explanation:

From the question we are told that

The sample size is
n = 25

The mean is
$\= x = 310 \ mg$

The standard deviation is
$\sigma = 36 \ mg$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

=>
$\alpha = 5\%$

=>
$\alpha = 0.05$

Next we obtain the critical value of
$(\alpha )/(2)$ from the normal distribution table , the value is

$Z_{(\alpha )/(2) } =Z_{(0.05 )/(2) } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{(\alpha )/(2) } * (\sigma )/(√(n) )$

substituting values

E = 1.96 * (36 )/(√(25) )

E = 14.1

The 95% level of confidence interval is mathematically represented as

$\= x - E < \mu<\ \= x - E$

substituting values

$310- 14.1 < \mu< 310+ 14.1$

$295.9 < \mu< 324.1$

The 95% level of confidence mean that there is 95% chance that the true population mean will be in this interval